I see anywhere from 15-25 dogs and cats on a Saturday. Yeah. I run ragged. During the week, the number is usually less. I usually only have one tech, so procedures that require sedation are out for Saturday, and if a dog is real trouble, we reschedule them.
Some vets will see anything that comes in the door, others see only dogs and cats, some even just see cats...or pocket pets...or horses. I also worked in the government for a while, and in that job, I managed import and export of animals and and animal products as well as working in eradicating disease outbreaks and performing trace backs on disease outbreaks. Also managed some large scale animal disease monitoring programs in my area and did a lot of teaching to farmers and owners. Fun stuff. Some friends if mine only do surgery, one works at a spay/neuter clinic. Another works in an emergency clinic. So vets don't only work in private practice and many have done several things in their career.
VPI has a list on their website about the 10 most common problems they reimburse for. That list is fairly representive in general. I see the following, but in no specific order, most often:
Dermatologic issues, such as flea allergies, hot spots, allergies, ear problems, skin masses
Vomiting, secondary to gastritis or foreign bodies but can be almost anything
Diarrhea, usually secondary to dietary indiscretion or colitis, sometimes parvo, other causes
Parvo
Intestinal parasites
Cancer
limping, which has 1001+ causes
Dental issues
Weight problems..ok, most people don't call for an appointment because their dog is fat, but I find this as the most common problem on examination, secondary to dental issues the owner did not realize were present. 45% or thereabouts of all pets are overweight, and 80% or so have dental disease by 3-4 years of age.
Toe nail trims and anal glands
But the TOP reason people bring animals in...wellness checks. And that is a GOOD thing.